This book provides a concise, approachable description of how modern NMR experiments work, aimed principally at those who use, or might use, an NMR spectrometer and are curious about why the spectra look the way they do. It provides, in an accessible and relatively informal fashion, the conceptual and theoretical tools needed to understand the inner workings of some of the most important multi-pulse, multi-nuclear, multi-dimensional techniques that chemists and biochemists use to probe the structures and dynamics of molecules in liquids. Part A (chapters 1-6) starts with the vector model, and proceeds to the more powerful product operator formalism. Part B (chapters 7-10) shows how straightforward quantum mechanics can be used to understand NMR and product operators at a more fundamental level. The treatment builds on material in P.J. Hore's OCP 32, Nuclear Magnetic Resonance, but it can also be used as a stand-alone text.